Google defines paradox in three ways, the first two being:
a statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory.
a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true.
These are almost opposite definitions. My English book defined it as the second, but I've always understood it to mean the first. Which is the most common usage?